Kati8/ICLR_2023_2025 huggingface dataset:
authors: Zhenyi Zhang
authors: Tiejun Li
authors: Peijie Zhou
reviews: 
Comments: This paper introduces DeepRUOT, a method for reconstructing dynamics from snapshots using regularized unbalanced optimal transport. This work tackles both the unbalanced and stochastic settings simultaneously, which few works have attempted thus far. An algorithm is proposed to learn drift, score, and growth functions from snapshot data including both synthetic and single-cell transcriptomics data.
Strengths: * Provided code provides additional clarity on experimental setting.
* Tackles an important problem in trajectory inference from population level data.
Weaknesses: * I found it extremely difficult to understand the multistage training procedure for DeepRUOT. There are some stages described in the main text, but then initial log density training also in the appendix? While there are a number of losses and initializations proposed to stabilize training, it is unclear to me what effects these have on final performance and how difficult RUOT is to train in practice. The paper would be much stronger if it was made clear which parts of the training procedure are important practically potentially through an ablation study on different components of the training procedure. 
* For a largely empirical work proposing a new algorithm to tackle this problem, the empirical studies are limited. The DeepRUOT is only benchmarked against balanced transport methods. It would greatly strengthen this paper if it was also compared to other unbalanced transport methods such as Action matching [Neklyudov et al. 2023] and unbalanced diffusion Schrödinger bridge [Pariset et al. 2023]. It would also be very useful to know how the many different weighting parameters affect performance, and how sensitive training is to them.
* It is difficult to tell what parts of the theory are novel and which are minor adaptations from prior work. Theorem 4.1 seems like a subclass of Baradat & Lavenant for the Fischer information case. I don’t believe varying sigma(t) over time changes anything theoretically and as far as I understand it is not used in practice.
Recommendation: 8
Reviewer confidence: 5
Soundness/correctness: 3
Clarity: 2
reviews: 
Comments: The paper introduces DeepRUOT, a new deep-learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. The method models dynamics without requiring prior knowledge of growth and death processes, allowing these to be learned directly from data through a Fisher regularization formulation. The authors explore theoretical connections between RUOT and the Schrödinger bridge problem while reformulating RUOT to transform stochastic differential equations into more computationally tractable ordinary differential equations (a constraint). When tested on both synthetic gene regulatory networks and real single-cell RNA sequencing data, DeepRUOT outperformed existing methods in constructing meaningful developmental landscapes.
Strengths: - The experimental results seem very convincing
- The paper provides thorough theoretical foundations with formal theorems and proofs connecting RUOT to the Schrödinger bridge problem.
Weaknesses: - it remains unclear how the loss function weights (cost, reconstruction error and the PINN loss) are set
- Figure 1 and its caption are not that helpful

Typos:
- Theorem 3.1: "probelm" -> "problem"
- page 8: "a increase" -> "an increase"
Recommendation: 10
Reviewer confidence: 2
Soundness/correctness: 3
Clarity: 3